Find the derivative of this function:

y=sin(cosx)

Any help would be appreciated.

y=sinu where u is cosx

dy/dx=cosu du/dx= cosu * -sinx
= -cos(cosx)*sinx

Oh, thanks. That makes it much easier. Didn't actually notice the cos(x) as being u.

To find the derivative of the function y = sin(cos(x)), you can use the chain rule. The chain rule states that if you have a composite function, like sin(cos(x)), the derivative can be found by taking the derivative of the outer function multiplied by the derivative of the inner function.

Here are the steps to find the derivative of y = sin(cos(x)):

1. Let's define u = cos(x). This way, our function can be rewritten as y = sin(u).

2. Take the derivative of u with respect to x. Since u = cos(x), du/dx = -sin(x).

3. Now, take the derivative of y = sin(u) with respect to u. The derivative of sin(u) with respect to u is simply cos(u).

4. Now, multiply the two derivatives we found: du/dx * dy/du. So, (-sin(x)) * cos(u).

5. Finally, substitute u back into the equation. Since we let u = cos(x), our derivative becomes (-sin(x)) * cos(cos(x)).

Therefore, the derivative of y = sin(cos(x)) is (-sin(x)) * cos(cos(x)).

It's important to note that in this explanation, we used the variable u for clarity while applying the chain rule. In the final answer, we substituted back the original function for u, resulting in (-sin(x)) * cos(cos(x)).